Magnetization characteristic of iron core with AC excitation

When an iron core is excited from an ac source, B and H vary cyclically. The ac magnetisation characteristic is the curve of peak flux density $B_m$ against peak magnetising force $H_m$ (or $\phi_m$ against $I_m$), obtained by joining the tips of the hysteresis loops traced at different excitation levels. It shows how the core magnetises under ac and gives its permeability and saturation.

Obtaining the characteristic

   B
   |             ___  saturation
   |         _.-' 
   |       /   (tips of loops)
   |     /:  
   |    / :  <- knee
   |   /  :
   |  /    linear region
   | / 
   |/  
 --+------------------- H
   |

1. A coil on the core is fed from a variable ac voltage at fixed frequency.
2. For a given voltage, the core goes round a hysteresis loop between $\pm B_m$ and $\pm H_m$. Since $V \approx 4.44 f N \phi_m$, $B_m$ is fixed by the voltage.
3. The voltage is raised step by step; each time a bigger loop is traced.
4. The curve through the tips $(H_m, B_m)$ of all the loops is the ac (normal) magnetisation curve.

Regions of the curve

• Initial region: at very low H the slope is small (domains move reversibly).
• Linear region: B rises almost in proportion to H; permeability is high and nearly constant. Machines and transformers are designed to work just below the knee.
• Knee: the slope falls as domains approach full alignment.
• Saturation region: further H gives very little increase in B; $\mu_r$ falls towards 1.

Features under ac excitation

• Hysteresis: each cycle traces a loop of area $\oint H\,dB$, giving loss $P_h = \eta B_m^{1.6}fV$.
• Eddy currents widen the dynamic loop further, and total core loss $P_c = P_h + P_e$ appears as the core-loss component of exciting current.
• Non-sinusoidal current: if the voltage (and so flux) is sinusoidal, the non-linear curve makes the magnetising current peaky with strong 3rd harmonic, especially near saturation.
• Apparent (ac) permeability $\mu = B_m/H_m$ varies with excitation level, being highest near the knee.

Use

The curve is used to choose the working flux density (about 1.2–1.7 T for silicon steel), to find the magnetising current for a given voltage, and to judge how much over-voltage a transformer can take before saturating.